On the infrared freezing of perturbative QCD in the Minkowskian region

Journal Article · Sun May 01 04:00:00 EDT 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.71.094017· OSTI ID:20709376

Caprini, Irinel; Fischer, Jan ^[1]

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1. National Institute of Physics and Nuclear Engineering, Bucharest POB MG-6, R-077125 (Romania)

The infrared freezing of observables is known to hold at fixed orders of perturbative QCD if the Minkowskian quantities are defined through the analytic continuation from the Euclidean region. In a recent paper [D. M. Howe and C. J. Maxwell, Phys. Rev. D 70, 014002 (2004)] it is claimed that infrared freezing can be proved also for Borel-resummed all-orders quantities in perturbative QCD. In the present paper we obtain the Minkowskian quantities by the analytic continuation of the all-orders Euclidean amplitudes expressed in terms of the inverse Mellin transform of the corresponding Borel functions [I. Caprini and M. Neubert, J. High Energy Phys. 03 (1999) 007]. Our result shows that if the principle of analytic continuation is preserved in Borel-type resummations, the Minkowskian quantities exhibit a divergent increase in the infrared regime, which contradicts the claim made in [D. M. Howe and C. J. Maxwell, Phys. Rev. D 70, 014002 (2004)]. We discuss the arguments given in this paper and show that the special redefinition of Borel summation at low energies adopted there does not reproduce the lowest order result obtained by analytic continuation.

• OSTI ID: 20709376
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 9 Vol. 71; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
EUCLIDEAN SPACE
MELLIN TRANSFORM
MINKOWSKI SPACE
PERTURBATION THEORY
QUANTUM CHROMODYNAMICS